I currently have a valid multiple entry Schengen visa that expires on Feb 10th (issued by the Spanish consulate). I need to visit the Czech Republic from Feb 9th to Feb 15th. For this, I am getting a visa starting Feb 11th from the Czech consulate as I was advised that I cannot have two simultaneous visas.

Is it possible for me to enter Czech republic on the current visa on Feb 9th, and stay past its expiry up to Feb 15th using the new visa without leaving the Czech Republic? Will there be any likely problem either while entering or exiting Schengen zone (I am entering Schengen in Frankfurt)?

Example: A Moroccan lawyer representing a gender equality NGO who frequently
participates in meetings in various Member States holds a multiple-entry-visa which expires
on 31.5. She applies for a new visa on 15.4.

If a new visa is issued, it should be valid from 1.6. and in such a case the visa holder would be entitled to enter the territory of the Member States on the basis of the first visa that will expire during the stay and leave on the basis of the new visa.